What Is the Change in the Velocity of a Railroad Car When a Man Jumps Off?

[relative rebound]

As i was doing a chapter review, I came across this question. I have tried to solve it, to now avail, I do not know where to begin. No solution was given in the textbook, and I would like to know how to solve it. Thanks for taking your time to help me.


Question:
A railroad flatcar of weight W can roll without friction along a straight horizontal track.. A man of weight w is standing on the car, which is moving to the right with a speed v. What is the change in the velocity of the car if the man runs to the left so that his speed relative to the car is V_rel just before he jumps off the left end?

 

[Chen]

Sounds like a momentum question. The momentum of the system is conserved, so:

v(W + w) = uW + (u - V_rel)w

Where:
v - velocity of the car before the man started running
W - the weight of the car
w - the weight of the man
u - velocity of the car once the man is running
V_rel - relative velocity of the man and car

All you have to do is solve for u.

 

[st3dent]

When I solve for u, i get

u = v_o + (V_relw) / (W + W)

 

[Chen]

I assume you meant to divide by (W + w). If so, then yes. You can see that the speed of the car increased. That is because the man "pushed" the car when he began to run, thereby accelerating it further.

 

[relative rebound]

Thanks for your help...It is much appreciated. I understand now.